Computing separable functions via gossip
Damon Mosk-Aoyama, Devavrat Shah · 2006
Motivated by applications to sensor, peer-to-peer, and ad-hoc networks, we study the problem of computing functions of values at the nodes in a network in a totally distributed manner. In particular, we consider separable functions, which can be written as linear combinations or products of functions of individual variables. The main contribution of this paper is the design of a distributed algorithm for computing separable functions based on properties of exponential random variables. We bound the running time of our algorithm in terms of the running time of an information spreading algorithm used as a subroutine by the algorithm. Since we are interested in totally distributed algorithms, we consider a randomized gossip mechanism for information spreading as the subroutine. Combining these algorithms yields a complete and simple distributed algorithm for computing separable functions. The second contribution of this paper is a characterization of the information spreading time of the gossip algorithm, and therefore the computation time for separable functions, in terms of the conductance of an appropriate stochastic matrix. Specifically, we find that for a class of graphs with small spectral gap, this time is of a smaller order than the time required to compute averages for a known iterative gossip scheme [4]. 1